DDoS attacks on cloud computing infrastructures are the same as DDoS attacks on any other environment. The difference is the impact; in the former case the cloud infrastructure as well as the customers it serves are affected; in the latter case, only the enterprise is affected.
Secondly, there is no such thing as a persistent DDoS attack per se. DDoS attacks may take some period of time, but persistence is used to categorize other attacks.
Thirdly, what do you mean by quantitative approach? do you refer to volume based control? or something else? Also, genetic algorithms?
A DDoS (or DoS) attack is always best mitigated on the hop above. If your link is flooded, then you will have a problem. However, if your provider cannot offer the level of protection required, then you can opt for solutions that incorporate two important aspects:
1. Volumetric control - block DDoS attacks based on traffic volume
2. Anomaly detection - block DDoS attacks based on identified anomalies in the traffic pattern.
Irrespective of whether you will find a solution covering point 1 or 2 above, or both, two very important factors must also be considered:
a. notification of the upstream provider - e.g. BGP blackholing of the subnet attacking you
b. traffic splitting (some may give it a different name) - block only DDoS traffic but let legitimate traffic pass through
All in all, cloud is yet another infrastructure that needs protection. I would personally go for a DPI (deep packet inspection) solution incorporating DDoS mitigation. This way, I could be covering all points above.